aiqbench analysis
This research identifies a critical optimization imbalance in sequential LLM quantization where Mean Squared Error (MSE) loss functions generate uneven gradients across stages, leading to suboptimal parameter updates. The authors propose using Root Mean Squared Error (RMSE) variants as a drop-in replacement that implicitly normalizes gradients, significantly improving accuracy without architectural changes. For practitioners implementing post-training quantization, this finding offers a direct methodological upgrade to standard loss functions to ensure balanced optimization throughout the model's layers.
The Devil Is in the Reconstruction Loss Scale: Rethinking Optimization in LLM Quantization
arXiv:2610.00983v1 Announce Type: cross Abstract: Post-training quantization (PTQ) methods typically use sequential quantization that partitions a pre-trained LLM into a series of units (e.g., transformer blocks), with one unit quantized at each stage. State-of-the-art PTQ methods are predominantly learning-based, optimizing auxiliary quantization parameters (e.g., scaling factors, rotation matrices, clipping thresholds, and adapters) via gradient descent to minimize a reconstruction loss. A common practice is to use mean squared error (MSE) as the reconstruction loss function, yet its induced optimization behavior remains largely unexplored. In this work, we take a holistic view of sequential quantization and systematically investigate how optimization evolves from the first quantization stage to the last, aiming for a deep understanding of optimization in learning-based PTQ schemes. Through extensive empirical studies spanning representative learning-based PTQ methods, LLM families, model scales, architectures, quantization settings and various tasks, we consistently uncover Optimization Imbalance: reconstruction loss magnitudes vary dramatically across stages, accompanied by highly uneven gradient magnitudes and parameter updates under MSE. We term the cross-stage range of loss magnitudes the reconstruction loss scale, and reveal that MSE translates the unexpectedly large reconstruction loss scale into highly uneven gradient magnitudes, which in turn lead to uneven optimization strength across quantization stages. This finding suggests a general principle for improving learning-based PTQ: optimization strength across stages should be decoupled from the reconstruction loss scale. Theoretically, we show that root mean squared error (RMSE) variants defined at the sample, channel, token, and element levels naturally realize this principle through implicit gradient normalization, outperforming MSE significantly as a drop-in replacement.
Abstract:Post-training quantization (PTQ) methods typically use sequential quantization that partitions a pre-trained LLM into a series of units (e.g., transformer blocks), with one unit quantized at each stage. State-of-the-art PTQ methods are predominantly learning-based, optimizing auxiliary quantization parameters (e.g., scaling factors, rotation matrices, clipping thresholds, and adapters) via gradient descent to minimize a reconstruction loss. A common practice is to use mean squared error (MSE) as the reconstruction loss function, yet its induced optimization behavior remains largely unexplored. In this work, we take a holistic view of sequential quantization and systematically investigate how optimization evolves from the first quantization stage to the last, aiming for a deep understanding of optimization in learning-based PTQ schemes. Through extensive empirical studies spanning representative learning-based PTQ methods, LLM families, model scales, architectures, quantization settings and various tasks, we consistently uncover Optimization Imbalance: reconstruction loss magnitudes vary dramatically across stages, accompanied by highly uneven gradient magnitudes and parameter updates under MSE. We term the cross-stage range of loss magnitudes the reconstruction loss scale, and reveal that MSE translates the unexpectedly large reconstruction loss scale into highly uneven gradient magnitudes, which in turn lead to uneven optimization strength across quantization stages. This finding suggests a general principle for improving learning-based PTQ: optimization strength across stages should be decoupled from the reconstruction loss scale. Theoretically, we show that root mean squared error (RMSE) variants defined at the sample, channel, token, and element levels naturally realize this principle through implicit gradient normalization, outperforming MSE significantly as a drop-in replacement.
Computation and Language (cs.CL); Artificial Intelligence (cs.AI)
arXiv:2610.00983 [cs.CL]
(or arXiv:2610.00983v1 [cs.CL] for this version)
https://doi.org/10.48550/arXiv.2610.00983 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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